To calculate the odds of the event occurring, we'll first find the total number of favorable outcomes and then divide it by the total number of possible outcomes.
1. Total Favorable Outcomes:
First, we need to determine the number of ways to choose 4 cards from one suit. Since each suit has 13 cards, this can be calculated as a combination of 13 cards taken 4 at a time, denoted as C(13, 4). So, the total number of ways to choose 4 cards from one suit is:
C(13, 4) = (13!)/(4!(13-4)!) = 715.
Next, we need to determine the number of ways to choose 3 cards from another suit. Again, this can be calculated as a combination of 13 cards taken 3 at a time, denoted as C(13, 3). So, the total number of ways to choose 3 cards from another suit is:
C(13, 3) = (13!)/(3!(13-3)!) = 286.
Now, we'll multiply the number of ways to choose 4 cards from one suit by the number of ways to choose 3 cards from another suit: 715 * 286 = 204,590.
Therefore, the total number of favorable outcomes is 204,590.
2. Total Possible Outcomes:
To find the total number of possible outcomes, we need to calculate the number of ways to choose 7 cards from a deck of 52 cards. This can be calculated as C(52, 7):
C(52, 7) = (52!)/(7!(52-7)!) = 133,784,560.
Therefore, the total number of possible outcomes is 133,784,560.
3. Calculating the Odds:
To find the odds, we divide the total number of favorable outcomes by the total number of possible outcomes and express it as a ratio.
Odds = Total Favorable Outcomes / Total Possible Outcomes
Odds = 204,590 / 133,784,560
Simplifying the ratio, we get:
Odds = 99 / 16,722,971
So, the odds of drawing 4 cards from one suit and 3 cards from another suit from a deck of 52 playing cards is 99/16,722,971.